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NCERT Exemplar · Class 10 Mathematics Area Related to Circles

60 questions · 60 still being checked

EXERCISE 11.2 11–14 (part 3 of 7)

  1. Exercise 11

    Is the area of the largest circle that can be drawn inside a rectangle of length a\displaystyle a cm and breadth b\displaystyle b cm (a>b)\displaystyle (a>b) is πb2 cm2\displaystyle \pi b^2 \mathrm{~cm}^2 ? Why?

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    NCERT’s printed answer for this exercise does not match its own question. This working follows the question as printed.

    False.The largest circle inside the rectangle is limited by the shorter side \(\displaystyle b\), so its diameter is \(\displaystyle b\): \[\text{radius}=\frac{b}{2} \] \[\text{Area}=\pi\left(\frac{b}{2}\right)^2=\frac{\pi b^2}{4} \] NCERT_Solution_Class10_Maths_Exemplar_Ch11_Ex11-2_Q11 The area is \(\displaystyle \dfrac{\pi b^2}{4} \) cm\(\displaystyle ^2\), not \(\displaystyle \pi b^2\) cm\(\displaystyle ^2\).

  2. Exercise 12

    Circumferences of two circles are equal. Is it necessary that their areas be equal? Why?

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    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    Yes, their radii are equal
    True.Circumference fixes the radius uniquely: \[C=2\pi r \implies r=\frac{C}{2\pi} \] Equal \(\displaystyle C\) forces equal \(\displaystyle r\), hence equal area: \[A=\pi r^2 \] So equal circumferences must give equal areas.

  3. Exercise 13

    Areas of two circles are equal. Is it necessary that their circumferences are equal? Why?

    Matches the book, not yet reviewed

    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    Yes, their radii are equal
    True.Area fixes the radius uniquely: \[A=\pi r^2 \implies r=\sqrt{\frac{A}{\pi}} \] Equal \(\displaystyle A\) forces equal \(\displaystyle r\), hence equal circumference: \[C=2\pi r \] So equal areas must give equal circumferences.

  4. Exercise 14

    Is it true to say that area of a square inscribed in a circle of diameter p cm\displaystyle p \mathrm{~cm} is p2 cm2\displaystyle p^2 \mathrm{~cm}^2? Why?

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    This working reaches the answer NCERT prints. It has not yet been read through by hand.

    NCERT’s answer
    No, diagonal of the square is \(\displaystyle p \mathrm{~cm}\).
    False.The diagonal of the inscribed square equals the circle's diameter \(\displaystyle p\): \[s\sqrt{2}=p \implies s=\frac{p}{\sqrt2} \] \[\text{Area}=s^2=\frac{p^2}{2} \] NCERT_Solution_Class10_Maths_Exemplar_Ch11_Ex11-2_Q14 The area is \(\displaystyle \dfrac{p^2}{2} \) cm\(\displaystyle ^2\), not \(\displaystyle p^2\) cm\(\displaystyle ^2\).